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Maru [420]
3 years ago
7

PLS HELP QUESTION 8 ANSWER CHOICES ARE ON THE PICTURE :(((g

Mathematics
1 answer:
Alborosie3 years ago
4 0

Answer:

11.125 meters i think it helps

Step-by-step explanation:

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Which is the equation of a hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0)? y squared over 40 minus x square
N76 [4]

The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is \frac{x^2}{10} + \frac{y^2}{15} = 1

<h3>How to determine the equation of the hyperbola?</h3>

The given parameters are:

  • Directrices at x = ±2
  • Foci at (5, 0) and (−5, 0)

The foci of a hyperbola are represented as:

Foci = (k ± c, h)

The center is:

Center = (h,k)

And the directrix is:

Directrix, x = h ± a²/c

By comparison, we have:

k ± c = ±5

h = 0

h ± a²/c = ±2

Substitute h = 0 in h ± a²/c = ±2

0 ± a²/c = ±2

This gives

a²/c = 2

Multiply both sides by c

a² = 2c

k ± c = ±5 means that:

k ± c = 0 ± 5

By comparison, we have:

k = 0 and c = 5

Substitute c = 5 in a² = 2c

a² = 2 * 5

a² = 10

Next, we calculate b using:

b² = c² - a²

This gives

b² = 5² - 10

Evaluate

b² = 15

The hyperbola is represented as:

\frac{(x - k)^2}{a^2} + \frac{(y - h)^2}{b^2} = 1

So, we have:

\frac{(x - 0)^2}{10} + \frac{(y - 0)^2}{15} = 1

Evaluate

\frac{x^2}{10} + \frac{y^2}{15} = 1

Hence, the equation of the hyperbola is \frac{x^2}{10} + \frac{y^2}{15} = 1

Read more about hyperbola at:

brainly.com/question/3405939

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6 0
2 years ago
Use the given root to find the remaining root of the function. Root: x = - 3 Function: f(x) = x ^ 2 + x - 6
ra1l [238]

Answer:

x = 2

Step-by-step explanation:

Since we know one root is -3, we know one factor of the equation is (x+3)

From there we can use the factor we know to factor the rest of the equation:

x^2 + x - 6 = (x+3) * ?

Since know -6 is just 3 * -2 and since 3-2 is 1,

(x+3)(x-2) = x^2 + x - 6

From there,

x - 2 = 0

x = 2

6 0
3 years ago
Elliot has been running a lawn care business since 2000. He cuts grass, trims, and weed whacks yards for his customers throughou
slamgirl [31]
Alright, we know that the slope intercept form is y=mx+b, where x and y remain variables, m stands for the slope and b stands for the y intercept. 

Because you should already have the slope from the first part (because slope is the same thing as rate of change), you should know that the slope is 60. The y-intercept should be your y value when x=0, and if you set up the equation in terms of years since Elliot has started his business, the year 2000 should be equal to x=0, so the y intercept should be equal to 750.

Now that you know the slope intercept form and what each part of it means, you can plug in what you have to get the final equation, which should be y=60x+750
6 0
3 years ago
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Find the measure of angle a.
Ostrovityanka [42]

Answer:

a = 127°

Step-by-step explanation:

The 3 angles lie on a straight line and have a sum of 180°, that is

15° + a + 38° = 180°

53° + a = 180° ( subtract 53° from both sides )

a = 127°

3 0
3 years ago
Who was the first president of the United States
Phoenix [80]

Answer: George Washington


Step-by-step explanation:


3 0
3 years ago
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